  # Country Boy

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1. No, "Jello" is a brand name- for a type of gelatine, not jelly. (Unless "jelly" is used in England to mean gelatine rather than a fruit spread for bread.)
2. y as a function of x, yes, $$y= a cosh\left(\frac{x}{a}\right)$$. But this is s, the arclength, as a function of $$\phi$$, then y as a function of x, yes- y= a cosh(x/a). But this is s, the arclength, as a function of phi, the angle the graph makes with the x-axis. It is the "Wethwell equation"- Catenary - Wikipedia
3. Notice that the author does NOT use the same "dot" for multiplication and a decimal point. Multiplication is indicated by a centered dot ($2\cdot 4$) while the decimal point is on the baseline (2.4).
4. You, yourself, said, in your first post, "The author uses a dot for multipllication and as a divider between the ones column and the tenths column" (I would have said "as a decimal point"). In this problem the author is using it as a decimal point but you are interpreting it as a multiplication.
5. It's not a matter of gravity suddenly "kicking in". A tiny mass produces a tiny gravitational force. Two very tiny masses will move toward each very slowly but with slowly increasing speed. Two larger masses will move toward each other with greater acceleration. It's simply a matter of when you are able to notice the acceleration. That depends on you not the mass.
6. Yes, an "endothermic" reaction ((1) endothermic reaction definition - Bing) is one that takes heat from the environment, so feels cold. An "exothermic" reaction ((1) exothermic reaction definition - Bing) is one that produces heat.
7. I have no idea whaty you are trying to say or what you are trying to ask. But certainly "200 ul" is NOT equal to "160 ul"! You say the ratio is "1/5000", "1/500", "1/250" OF WHAT? Apparently you want the "volume of antibody" to be 1/5000 or SOMETHING but 1/5000 or WHAT? My best guess at what you are trying to say: 1/5000 of something is 200 ul so the "something" is 200(5000)= 1000000 ul or 1 l. 1/500 or that 0. ul or l. 1/250 of that is 4000 ul or 0.004 l. (I assume your "ul" is a good replacemet for $\mu l$ or "microliters", one millionth of a liter.)
8. ## Understanding the Equation of Monte Carlo Method returning value to the expected function

You should state that the three values of X are assumed to have equal probability so P(-1)= P(0)= P(1)= 1/3. Then E(g(x))= g(-1)/3+ g(0)/3+ g(1)/3= 0/3+ 1/3+ 2/3= 1. Zak100, it is not the "expected function" but the "expected value" of the function.
9. The verb is "affect", "effect" is a noun. Gravity "affects" time and thus has an "effect" on time.
10. "c/t" has unit of "distance over time squared" so is an acceleeration, not a distance.
11. Think about the angle your legs make with smaller steps rather than longer steps. Both legs with be more nearly vertical at all times so will have a larger normal force.
12. Sorry. I missed the word "open" in the original question. Yes, a non-empy OPEN set in a measure space is necessarily of positive measure.
13. The first statement is not true. For example, a singleton set has 0 measure. What is true that any set containing an interval has non-zero measure.
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